The Cubs won't rush Baker, who has pitched all or part of seven seasons with the Twins, from 2005-11, totaled 28 or more starts in three straight seasons, 2008-10.
Baker was already beginning to throw and said his plan is to use the Spring Training starts as part of his rehab process. He did get interest from other teams, including the Twins.
"It's a big season for me personally coming off an injury," Baker said. "I wanted somewhere where my family could enjoy and we could have a lot of fun and I could help the team be productive."
Epstein called Baker an "underrated pitcher" and someone who does things they value, among them not walking batters.
"Scott Baker is a pitch maker," Epstein said. "He's somebody who can go out and execute a game plan against the best lineups. When he's commanding and healthy, he'll have a lot of success in this division."
The Twins' Opening Day starter in 2010, Baker was limited to 23 appearances in 2011 because of a right elbow injury that eventually required Tommy John surgery. He did not pitch last year.
Baker leaves the Twins ranked among the club's all-time leaders in several categories, including winning percentage (.568, fourth, minimum 100 decisions), starts (11th with 159), wins (11th with 63) and strikeouts (11th with 770).
Baker is the second pitcher the Cubs have acquired who has undergone Tommy John surgery last year, joining Arodys Vizcaino, who was acquired from the Braves for Paul Maholm.
"You don't set out looking for Tommy John guys," Epstein said. "The reality is it's not exactly a buyer's market for pitching so you have to take your risks. Do you want to take a risk on a guy with bad makeup? Do you want to take a risk on a guy with bad command? Or do you want to take the risk on a guy you really believe in who is coming off Tommy John surgery and has appropriate value points? I think we're very comfortable placing our bet on Scott Baker."
The success rate for pitchers who have had Tommy John surgery is high. Baker also is realistic.
"I'm not going to promise 20 wins and 200 innings," Baker said. "I haven't pitched in a year, I didn't pitch obviously last season, and it's going to be tough, but I'm willing to put in the work."